tag_mem_smul_span — Mathlib

English

The tag of ν lies in the scaled lattice: tag n ν ∈ (n)⁻¹ • L.

Русский

Тег ν лежит в L-образной сплющенной решетке: tag n ν ∈ (n)⁻¹ • L.

LaTeX

$$$$ \mathrm{tag}\, n\, \nu \in (n:\\mathbb{R})^{-1} \cdot L $$$$

Lean4

theorem tag_mem_smul_span (ν : ι → ℤ) : tag n ν ∈ (n : ℝ)⁻¹ • L :=
  by
  refine mem_smul_span_iff.mpr fun i ↦ ⟨ν i + 1, ?_⟩
  rw [tag_apply, div_eq_inv_mul, ← mul_assoc, mul_inv_cancel_of_invertible, one_mul, map_add, map_one, eq_intCast]

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